Taiwanese Journal of Mathematics
- Taiwanese J. Math.
- Volume 15, Number 1 (2011), 283-305.
Some New Families of Generalized Euler and Genocchi Polynomials
The main object of this paper is to introduce and investigate a new generalization of the family of Euler polynomials by means of a suitable generating function. We establish several interesting properties of these general polynomials and derive explicit representations for them in terms of a certain generalized Hurwitz-Lerch Zeta function and in series involving the familiar Gaussian hypergeometric function. Finally, we propose an analogous generalization of the closely-related Genocchi polynomials and show how we can fruifully exploit some potentially useful linear connections of all these three important families of generalized Bernoulli, Euler and Genocchi polynomials with one another.
Taiwanese J. Math., Volume 15, Number 1 (2011), 283-305.
First available in Project Euclid: 18 July 2017
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Bernoulli polynomials Euler polynomials Genocchi polynomials Apostol-Bernoulli polynomials Apostol-Euler polynomials Apostol-Genocchi polynomials Hurwitz-Lerch Zeta function Gaussian hypergeometric function Stirling numbers of the second kind Taylor-Maclaurin series expansion Leibniz rule Pfaff-Kummer transformation Gauss summation theorem
Srivastava, H. M.; Garg, Mridula; Choudhary, Sangeeta. Some New Families of Generalized Euler and Genocchi Polynomials. Taiwanese J. Math. 15 (2011), no. 1, 283--305. doi:10.11650/twjm/1500406175. https://projecteuclid.org/euclid.twjm/1500406175